Velocity of a cork fired from a cork gun

  • Thread starter esoteric deviance
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In summary, the spring is compressed by 5.5 cm with a k value of 10 N/m and is used to propel a 3.8 g cork from a cork gun. For part A, the speed of the cork when released as the spring passes through its relaxed position is 2.82 m/s. For part B, using conservation of energy, the speed of the cork at the time of release is determined by setting the initial potential energy of the spring equal to the final potential energy of the spring plus the kinetic energy of the cork. After solving for v, the speed of the cork is determined to be _______ (insert numerical value here) m/s.
  • #1
esoteric deviance
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A spring is compressed by 5.5 cm and used to propel a 3.8 g cork from a cork gun. k = 10 N/m.

A) What is the speed of the cork if it is released as the spring passes through its relaxed position?

B) Suppose, instead, that the cork sticks to the spring and stretches it 1.5 cm before separation occurs. What now is the speed of the cork at the time of release?


For part A, I used the law of conservation of energy to get:
KE of the cork = PE of the spring​
(1/2)m(v^2) = (1/2)k(x^2)​
v = 2.82 m/s​


But for part B, I'm not sure what to do :frown:.
I know I need to use conservation of energy again, but I don't know how to set it up.
 
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  • #2
Hint: if the spring streches, it has an amount of potential energy stored in it.
 
  • #3
Still don't know what to do lol.

Unfortunately, I might need a bit more than a hint on this one.
Sadly, I've been trying to figure it for the past 45 min to no avail :(.

Maybe if you could show me how to set up the conservation thing and explain the reasoning behind it...
 
  • #4
Well, what does 1/2 k x^2 represent?
 
  • #5
the PE of the spring when it's compressed?
 
  • #6
esoteric deviance said:
the PE of the spring when it's compressed?

Right, when it's compressed and when it's streched. :smile:
 
  • #7
but wouldn't the values be different since the change in x when it's compressed is 5.5 cm and the change in x when it's stretched is 1.5 cm?
 
  • #8
The EPE initial (KE=0) = the combination of EPE and KE at any point. The problem would be the same whether the string was compressed 1.5 cm or stretched
 
  • #9
esoteric deviance said:
but wouldn't the values be different since the change in x when it's compressed is 5.5 cm and the change in x when it's stretched is 1.5 cm?

Yes, the values are different, and there is no problem here. Define two points. One is the point when the spring is compressed by 5.5 cm, and the other is the point when the spring is streched by 1.5 cm. Define energy (sum of kinetic and potential energy) for both of these points. Now set these energies equal (since energy is conserved), and solve for v.
 
  • #10
the thing is that I'm not sure how to do that.

is it something like
KE of the cork = final PE of spring - initial PE of spring?​
 
  • #11
esoteric deviance said:
the thing is that I'm not sure how to do that.

is it something like
KE of the cork = final PE of spring - initial PE of spring?​

Point 1: the spring posesses potential energy, the cork posesses no energy.

Point 2: the spring posesses some other potential energy, the cork posesses kinetic energy.

Energy at point 1 = Energy at point 2.
 
  • #12
so these are the points right|-----5.5 cm-----|--1.5 cm--|
1 2

(that 2 should be at the end of the line)

point 1 = initial
point 2 = final

so i get:
initial PE of spring + initial KE of cork = final PE of spring + final KE of cork

is that right?
 
Last edited:
  • #13
Yes, that is right. The 'initial' KE of the cork equals zero, of course. Now plug in the numbers and solve for v.
 
  • #14
thanks :smile:
 

Related to Velocity of a cork fired from a cork gun

1. What factors contribute to the velocity of a cork fired from a cork gun?

The velocity of a cork fired from a cork gun is affected by several factors, including the force used to fire the cork, the weight and size of the cork, and any external forces acting on the cork such as air resistance or gravity.

2. How can the velocity of a cork fired from a cork gun be measured?

The velocity of a cork fired from a cork gun can be measured using a velocity meter, which calculates the speed of an object by measuring the time it takes to travel a known distance. Another method is to use high-speed cameras to capture the motion of the cork and calculate its velocity.

3. Does the type of cork gun used affect the velocity of the cork?

Yes, the type of cork gun used can significantly impact the velocity of the cork. A cork gun with a longer barrel and a stronger spring or air pressure mechanism will typically fire the cork at a higher velocity compared to a shorter barrel or weaker mechanism.

4. Can the velocity of a cork fired from a cork gun be increased?

Yes, the velocity of a cork fired from a cork gun can be increased by using a more powerful firing mechanism, reducing the weight of the cork, or reducing external forces such as air resistance. However, it is important to note that increasing the velocity beyond a certain point can be dangerous and should be done with caution.

5. How does the velocity of a cork fired from a cork gun compare to other projectiles?

The velocity of a cork fired from a cork gun is relatively low compared to other projectiles such as bullets or rockets. However, it can still cause harm or injury if not handled properly. It is important to always follow safety precautions and use appropriate protective gear when firing a cork gun.

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